$i \times (j \times k) + j \times (k \times i) + k \times (i \times i)$ equals

If $a$ is a vector perpendicular to both $b$ and $c$,then

Statement $(A)$ : If $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{c}$,then $\vec{a} \times (\vec{b} \times \vec{c}) = 0$.
Reason $(R)$ : If $\vec{b}$ is perpendicular to $\vec{c}$,then $\vec{b} \times \vec{c} = 0$.

If three unit vectors $a, b, c$ are such that $a \times (b \times c) = \frac{b}{2},$ then the vector $a$ makes with $b$ and $c$ respectively the angles

If $\vec{a}$ and $\vec{b}$ are perpendicular,then $\vec{a} \times(\vec{a} \times(\vec{a} \times(\vec{a} \times \vec{b})))$ is equal to

Let $\vec{a}=-\hat{i}+\hat{j}+2\hat{k}$, $\vec{b}=\hat{i}-\hat{j}-3\hat{k}$, $\vec{c}=\vec{a}\times\vec{b}$ and $\vec{d}=\vec{c}\times\vec{a}$. Then $(\vec{a}-\vec{b}) \cdot \vec{d}$ is equal to :